 |
$\begin{align}(i)x+4&>11\\[5pt]
x+4-4&>11-4\\[5pt]
&\underline{\underline{x>7}}\end{align}$ | $\begin{align}(ii)y+3& \ge0\\[5pt]
y+3-3&\ge0-3\\[5pt]
&\underline{\underline{y\ge-3}}\end{align}$ | $\begin{align}(iii)p-5&<2\\[5pt]
p-5+5&<2+5\\[5pt]
&\underline{\underline{p<7}}\end{align}$ |
$\begin{align}(iv)p-3&>-1\\[5pt]
p-3+3&>-1+3\\[5pt]
&\underline{\underline{p>2}}\end{align}$ | $\begin{align}(v)a+5&\le1\\[5pt]
a+5-5&\le1-5\\[5pt]
&\underline{\underline{a\le-4}}\end{align}$ | $\begin{align}(vi)&5y<12\\[5pt]
\frac{5y}{5}&<\frac{12}{5}\\[5pt]
&\underline{\underline{y<2\frac{2}{5}}}\end{align}$ |
$\begin{align}(vii)-2x&\ge10\\[5pt]
\frac{-2x}{-2}&\le\frac{10}{-2}\\[5pt]
&\underline{\underline{x\le-5}}\end{align}$ | $\begin{align}(viii)-3y&<-9\\[5pt]
\frac{-3y}{-3}&>\frac{-9}{-3}\\[5pt]
&\underline{\underline{y>3}}\end{align}$ | $\begin{align}(ix)\frac{-2x}{3}&>6\\[5pt]
\frac{-2x}{3}\times 3&>6\times 3\\[5pt]
-2x&>18\\[5pt]
\frac{-2x}{-2}&<\frac{18}{-2}\\[5pt]
&\underline{\underline{x<-9}}\end{align}$ |
 |
$\begin{align}(i)x+3&\ge1\\[5pt]
x+3-3&\ge1-3\\[5pt]
&\underline{\underline{x\ge-2}}\end{align}$
 | $\begin{align}(ii)y-4&<-1\\[5pt]
y-4+4&<-1+4\\[5pt]
&\underline{\underline{y<3}}\end{align}$
 | $\begin{align}(iii)3x&>-3\\[5pt]
\frac{3x}{3}&>\frac{-3}{3}\\[5pt]
&\underline{\underline{x>-1}}\end{align}$
 |
$\begin{align}(iv)\frac{x}{2}&\le0\\[5pt]
\frac{x}{2}\times 2&\le0\times 2\\[5pt]
&\underline{\underline{x\le 0}}\end{align}$
 | $\begin{align}(v)-5y&>10\\[5pt]
\frac{-5y}{-5}&<\frac{10}{-5}\\[5pt]
&\underline{\underline{y<-2}}\end{align}$
 | $\begin{align}(vi)-4x&\ge12\\[5pt]
\frac{-4x}{-4}&\le\frac{12}{-4}\\[5pt]
&\underline{\underline{x\le-3}}\end{align}$
 |
 |
$\begin{align}(i)x+3&>7\\[5pt]
x+3-3&>7-3\\[5pt]
x&>4\\[5pt]
\end{align}$ | $\begin{align}(ii)x-3&<2\\[5pt]
x-3+3&<2+3\\[5pt]
x&<5\\[5pt]
\end{align}$ | $\begin{align}(iii)3x&>7\\[5pt]
\frac{3x}{3}&>\frac{7}{3}\\[5pt]
x&>2.33\\[5pt]
\end{align}$ |
$\begin{align}(iv)-2x&<8\\[5pt]
\frac{-2x}{-2}&>\frac{8}{-2}\\[5pt]
x&>-4\\[5pt]
\end{align}$ | $\begin{align}(v)5-x&>6\\[5pt]
5-x-5&>6-5\\[5pt]
-x&>1\\[5pt]
\frac{-x}{-1}&<\frac{1}{-1}\\[5pt]
x&<-1\\[5pt]
\end{align}$ | |
 |
$\begin{align}(i)x+1&>-2\\[5pt]
x+1-1&>-2-1\\[5pt]
x&>-3\\[5pt]
&\underline{\underline{\text{Smallest value of x is -2}}}\end{align}$
| $\begin{align}(ii)-3y&>15\\[5pt]
\frac{-3y}{-3}&<\frac{15}{-3}\\[5pt]
y&>-5\\[5pt]
&\underline{\underline{\text{Biggest value of y is -6}}}\end{align}$ | |
 |
$\begin{align}x+3&>1\\[5pt]
x+3-3&>1-3\\[5pt]
x&>-2\\[5pt]
\end{align}$
$\begin{align}2x&\le12\\[5pt]
\frac{2x}{2}&\le \frac{12}{2}\\[5pt]
x&\le6\\[5pt]
\end{align}$
 | | |